I've had this same problem with my Merrybunny - only both his eyes were watering. From what my vets (and people on the forum) have said it could be one of three things:
1) an infection
2) a blocked tear duct - this would need flushing out
3) his teeth roots are overgrown blocking his tear ducts. this could be very serious, but can only be checked with an x-ray, which of course has it's own risks.
Since it's only one eye, I'd think 1 or 2 are most likely. Best thing would be to take him to the vet who'll probably try him on some antibiotics as a first step.
I tried a couple of courses of antibiotics with Merry. Then recently we tried flushing his eyes and another course of antibiotics. his eyes have improved a lot, so I'm hoping that with another flushing/antibiotics course he'll be fully cured.